In optical communication systems, digital modulation techniques are used to convert digital information (i.e., bits) into symbols carried by optical signals (e.g., light pulses) through the optical fiber. Dispersion, or the spreading of optical signals as they travel down a fiber in time, can manifest changes in both time and frequency and makes it harder to distinguish the symbols at the receiver. Various solutions exist for dealing with optical dispersion, such as using signals at wavelengths with group velocity dispersion (GVD) equal to zero, using solution pulses in the regime of negative dispersion, or using opposite-sign dispersion fibers to cancel dispersion effects (details are outside the scope of this disclosure). However, compensating for dispersion (e.g., using GVD=0) can amplify other nonlinear effects in the optical pulses, which also make it hard to decode the symbols at the receiver. Examples of nonlinear effects include four wave mixing, where interactions between two or three wavelengths produce two new interfering wavelengths, and self-phase modulation, where variation in refractive index produce a phase shift in the optical pulse, leading to a change of the pulse's frequency spectrum.
Thus, dispersion and fiber nonlinearities are critical limiting factors on the data rates achievable by optical fiber communications systems. The increase in demand for broadband services call upon next generation optical transceivers to deliver over 1 terabit per second (Tbps) transmission rates over optical submarine links, which typically include thousands of kilometers of dispersion managed (DM) and dispersion unmanaged (UM) fiber optical cables. DM optical fiber cables use optical fibers with different amounts of dispersion, both positive and negative, distributed along the link for the purpose of obtaining zero to little dispersion at the receiver. UM fiber optical cables allow most of the accumulated dispersion to be compensated at the receiver. In all cases, coherent optical communication systems that are effectively robust to fiber nonlinearities are desirable.